HarryWatson94

Hello,
my wife is a UK citizen. We have a daughter together. Currently we’re waiting the approval of the I-130 with instructions to further complete the CR1. I just had one question. Because I am a US citizen and we’ve been back and forth so much, are we allowed to travel once the I-130 is approved and CR-1 is pending, do we then have to stay in the UK until it’s approved or is there something else I should apply for to allow travel? 
thank you so much 

So, you are absolutely allowed to travel after the I-130 is approved. Depending on your interpretation, CR-1 would only be "pending" while the passport has been handed over to the Consulate at the interview—it is therefore impossible to travel at this point as you will need your passport to travel. 
 
If you mean that your I-130 is approved and you haven't attended an interview yet, and you are travelling to the US, you will have to convince the border officer that you are not intending to stay. In my experience, being from an ESTA country, I have never been asked to provide proof or evidence of ties to my country of residence. For good measure, I carry a copy of my lease and employment contract with me, just in case. 
 

Transcripts show you filed taxes.
USCs and LPRs are required to file even if living abroad, so they don't do anything useful for domicile.
 
It sounds like NVC is passing through the documents but letting you know that intent to establish domicile has not been satisfied with the evidence presented. The CO makes the final decision.